Matrix

Eigenvectors: find eigenvalues, then solve

A−λI=0A−λI=0

Lagrange

ddt(∂L∂x˙)−∂L∂x=0\frac{d}{dt}\left(\frac{\partial{\mathcal{L}}}{\partial{\dot{x}}}\right)−\frac{\partial{\mathcal{L}}}{\partial{x}}=0

Structures

Euler Bernoulli

Euler-Bernoulli EquationEuler-Bernoulli Equation · ^Euler-Bernoulli-equation · Embedded block

EId2ydx2=F(x)EI\frac{d^2y}{dx^2}=F(x)

FEM

Bending Matrix

Axial Stress Matrix

K=[1−1−11]K= \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}


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